Coronavirus Optimization Algorithm: A Success-History Adaptive Evolutionary Framework with Archive-Assisted Search and Stagnation Recovery for Global Optimization

Hari Mohan Pandey

Figure 1: Viral-load dynamics as population-size reduction in COA. The left part illustrates the conceptual decrease in viral load across early, middle, and late stages. The right part gives the optimization role: the active population size is gradually reduced from

NP_{0}

to

NP_{min}

as the number of function evaluations increases. This reduction controls the shift from broad exploration to focused exploitation.

Figure 2: Spike–receptor binding as elite-guided attraction in COA. The biological motif of spike–receptor binding is translated into the search movement from the current solution

x_{i}

toward an elite solution

x_{pbest}

. The additional difference vector

x_{r_{1}}-\hat{x}_{r_{2}}

prevents purely greedy movement and helps maintain exploratory mobility.

Figure 3: Viral replication as mutation and binomial crossover. The figure describes how COA generates a new candidate solution. First, mutation creates a mutant vector

v_{i}

. Then, binomial crossover forms the trial vector

u_{i}

by selecting some dimensions from the mutant vector and the remaining dimensions from the parent vector

x_{i}

.

Figure 4: Antigenic drift as success-history adaptation of

F

and

CR

. The figure shows the adaptive loop used in COA. Successful trials contribute values to the memories

M_{F}

and

M_{CR}

, and future mutation and crossover parameters are sampled around these memories. This creates controlled exploratory variation rather than static or manually tuned parameter behaviour.

Figure 5: Immune evasion as opposition-based partial restart. The figure shows how COA replaces the weakest part of the population when stagnation occurs. Poor candidates are mapped to opposition-based alternatives inside the bounded domain, while stronger candidates and the best-so-far solution are preserved.

Figure 6: Overall flowchart of the Coronavirus Optimization Algorithm (COA). The flowchart integrates the full optimization pipeline: parameter initialization, opposition-based initialization, adaptive population-size control, stagnation detection, opposition-based partial restart, per-individual trial generation through mutation and crossover, greedy selection, archive update, and success-history memory update. It serves as a visual complement to Algorithm 2 and shows how the main operator blocks interact during one complete optimization run.

Operation	Time	Frequency per generation
Population sorting	$O(NP\log NP)$	1
Mutation (vector)	$O(D)$	$NP$
Crossover (vector)	$O(D)$	$NP$
Boundary projection	$O(D)$	$NP$
Objective evaluation	$C_{f}$	$NP$
Archive pruning	$O(NP)$	$\leq 1$

Table 3: Per-generation computational complexity of COA operations at population size

NP

.

Figure 7: Average Friedman ranking across 29 functions at

D=10

. Lower rank is better.

Figure 8: Signed

\log_{10}

mean objective-value heatmap across 29 CEC 2017 functions at

D=50

. The figure highlights COA’s robustness on composition functions and larger performance gaps on difficult high-dimensional functions.

Figure 9: Number of best or tied-best mean results per algorithm at

D=50

. Values in parentheses indicate strict wins.

Figure 10: Signed

\log_{10}

mean objective-value heatmap across 29 CEC 2017 functions at

D=10

. Stronger colour contrasts indicate functions where algorithmic differences are more pronounced.

Figure 11: Signed

\log_{10}

mean objective-value heatmap across 29 CEC 2017 functions at

D=30

. The composition functions F20–F29 show stable patterns, while selected hybrid functions remain more competitive.

Figure 12: Number of best or tied-best mean results per algorithm at

D=10

. Values in parentheses indicate strict wins.

Figure 13: Number of best or tied-best mean results per algorithm at

D=30

. Values in parentheses indicate strict wins.

Figure 14: Average Friedman ranking across 29 functions at

D=30

. COA remains the top-ranked method, followed by AO, CMA-ES, and JADE.

Figure 15: Average Friedman ranking across 29 functions at

D=50

. COA obtains its strongest average rank among the three tested dimensions.

Figure 16: Convergence profiles across 29 CEC 2017 functions at

D=10

.

Figure 17: Convergence profiles across 29 CEC 2017 functions at

D=30

. COA remains competitive in the larger search space and shows stable behaviour on composition functions.

Figure 18: Convergence profiles across 29 CEC 2017 functions at

D=50

. COA preserves strong aggregate convergence, although differences on hybrid functions remain visible.

Parameter	Value	Role and rationale
Dimensions	$D=10,30,50$	Tests low- and medium-dimensional behaviour.
Function evaluations	50,000; 300,000; 500,000	Budgets for $D=10$ , $D=30$ , and $D=50$ , respectively.
Independent runs	30	Provides repeated-run evidence for statistical comparison.
Initial population $NP_{0}$	30	Compact population retained after opposition-based initialization.
Minimum population $NP_{min}$	8	Maintains a small late-stage population for exploitation.
Memory size $H$	60	Stores successful parameter tendencies across generations.

Table 12: COA parameter values used in the experiments.

Algorithm	$D=10$	$D=30$	$D=50$
COA	$1.24\times 10^{-2}$	$8.91\times 10^{-2}$	$1.53\times 10^{-1}$
AO	$3.71\times 10^{-2}$	$1.42\times 10^{-1}$	$2.87\times 10^{-1}$
JADE	$4.56\times 10^{-2}$	$2.18\times 10^{-1}$	$4.02\times 10^{-1}$
CMA-ES	$2.89\times 10^{-2}$	$1.75\times 10^{-1}$	$3.14\times 10^{-1}$

Table 18: Mean standard deviation across 29 functions. Lower = more consistent.

Variant	Avg. rank	Rank loss vs. COA
COA (full)	2.86	—
COA ${}_{\text{noOpp}}$	4.12	+1.26
COA ${}_{\text{noArc}}$	5.83	+2.97
COA ${}_{\text{noSHA}}$	6.91	+4.05
COA ${}_{\text{noRes}}$	4.75	+1.89
COA ${}_{\text{noPop}}$	5.14	+2.28

Table 19: Ablation study at

D=30

: average Friedman rank across 29 functions.

$\gamma$	0.3	0.5	0.7 (default)	0.9	1.0	1.5
Avg. rank	4.18	3.42	2.86	3.15	3.67	5.23

Table 20: Sensitivity of COA average rank to

\gamma

at

D=30

.

Comparison	Min	Median	Max	$\lvert d\rvert>0.8$ count
COA vs. AO	$-2.14$	$-0.63$	$1.28$	12/29
COA vs. GWO	$-3.87$	$-0.91$	$2.45$	18/29

Table 21: Cohen’s

d

distribution for COA vs. AO and GWO at

D=30

. Negative favors COA.

Category	$\kappa\times 10^{3}$
Unimodal	8.42
Multimodal	3.17
Hybrid	1.84
Composition	2.53

Table 22: Average convergence rate

\kappa

over first 30% of generations at

D=30

.

Coronavirus Optimization Algorithm: A Success-History Adaptive Evolutionary Framework with Archive-Assisted Search and Stagnation Recovery for Global Optimization

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